Basicly. is not the "role" is more the lane position (You can go jungler as Fiddle(AP) and let mid for Urgot (AD) for example).

Solo top and Jungler are the one who carry the team through the early/mid game. mid is very important too.

So in order I would say:

Top

A good top lane is usually off-tank.

Controlling your top lane, give you the advantage being focused. (look at example Voliboy from team Dignitas). Being Focused cause the
opponent jungler being around a lot. what provide a defense to your
mid lane. Also give you the advantage to deny xp / gold to the
opponent off-tank. what will make unbalanced team fights.

Jungle

A good jungler is usually ad-carry/off-tank.

Controlling the jungle, you control the early game.

To control the jungle you need break the rhythm of the opponent jungler. Doing this, you are able to over level him. make his ganks
take longer, and probably less effective (Without red, or blue in some
cases). Know the jungler time, you need know when and where the
opponent probably is.

Make good ganks. Don't wait for level 6 or 11 (once i hear that... o.O) to gank someone else lane. Create the opportunity (Look at how M5
ganked Mordekaiser in the first final vs Dignitas).

Control of the Dragon and Baron is the most important task here. (Right beside gank)

AP Carry (mid)

Another good way is solo mid. but you start to depend sometime of someone else.

Remember get some good counter here. If the opponent is a Karthus, LeBlanc or Kass would be a little better than Ez for example.

Support is (in my opinion) the more important role in the game, but also the most dependent one. If you lane partner is not good (by not
good read, REALLY BAD) or if you don't get his time to start fights or
run from them. you will be underlevel, without mana, without cd.

Need to match with your AD Carry. Janna is great with Corki but would not be so great with Akali (ok, akali bot and ad carry is not a great example but...), in this case Taric, Alistar or Galio would be better (akali need someone to tank for her)

AD Carry (together with support)

Carry AD is what win the game (break turrets, nexus, etc), but is hard to break anything if your team fed, or if you can't get close to
any structure (no minions pushed, no tank for them). Usually I see BAD
AD carry's and Kamikaze ones.

As i said in support section. Combine with your support the champion, to pull great results.

Put simply you are wishing to master one of the five roles in the current meta game
AD
AP
Top
Jungle
Support

Most simply put the way that you view winning at this point is crushing and snowballing.
The best places to do this are
AP - mid
Top - bruiser

So in order to have most impact on the game in the first 20-30 minutes, Play those two.
Jungle and support also give lots of power over early game however it is in a less hands on instant gratification sort of way.

In my experience, the roles that can best control the outcome of the game are AP middle, jungle, and top solo with teleport. That being said, it also depends on the CHAMPION pick in order to control other lanes as well! Analyzing each role, we can determine which champions are the best at controlling the outcome of the game.

Top solo-
Realistically, you can pick any1 who is a strong early game ganker, and add teleport to the mix. An example would be yorick, or singed. The key is COMMUNICATION! Talk to your support and ad carry. Tell them to ward the brush closest to the enemy tower. When the enemy team overextends, not even extensive river warding can save them. Thats a potential double kill for your AD carry. Boom, you just nudged the game in your favour. This type of play can continue on through the game until youre team becomes terrifying. Lane is getting ganked? Teleport and even up that exchange. More often than not, it will work out and you've just showed everyone the power of a communication top laner.

Mid lane-
This is my favourite for sure! But it depends on the mobility of the champion. My favourite picks for determining the outcome of other lanes are twisted fate, ahri, and karthus. Those picks speak for themselves. Twisted fate= teleporting terror of gold cardiness. Ahri= the most mobile ap champ in the game, doesnt matter if they see u coming, they know their fate has been sealed. Karthus= Press R and uve just turned a 2v2 exchange into a 2vdead exchange. once again, youve just nudged the game in your direction. Another good example is sion with mobility boots. to summarize this paragraph- MOBILITY CONTROLS OTHER LANES AND WINS THE GAME!

Jungle-
Jungle speaks for itself, it is the ultimate role in which to screw with every person on the other team. But it takes practice, a good knowledge of game mechanics, and having the ability to realise when to gank and when to afkfarm. Junglers will get blamed if the lane is lost. This is the primary issue in my opinion, but theres a way around that. YOU ARE THE SMITING MACHINE. Nothing is more rewarding then a dirty smite steal on baron, or enemy buffs. I can't say this enough- PRACTICE SMITE STEALING. It WILL turn any game in your favour when you just singlehandedly got your team 1500 gold and baron buff.

Follow these tips, and you will surely win more than you lose. Just remember, there will always be bad people in the game who will lose their lane. Help em out anyway you can and the victory will be yours!